Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19104763 | C2 | semidirect |
| 2. #23782232 | C2 | semidirect |
| 3. C2×#19104731 | C2 | semidirect |
| 4. C2×#19104661 | C2 | semidirect |
| 5. #23781671 | C2 | semidirect |
| 6. #23781426 | C2 | semidirect |
| 7. C2×#100×C163 | C2 | semidirect |
| 34. C2×Dic326 | D4 | semidirect |
| 40. C2×D652 | D4 | semidirect |
| 41. C2×D652 | D4 | semidirect |
| 50. C4⋊Dic163 | D4 | semidirect |
| 55. C4×Dic163 | D4 | semidirect |
| 67. M16×C163 | D4 | semidirect |
| 138. C163 | #2002 | semidirect |
| 145. C2×#100 | D163 | semidirect |
| 200. M16 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104763 | 2 |
| #23782232 | 2 |
| C2×#19104731 | 2 |
| C2×#19104661 | 2 |
| #23781671 | 2 |
| #23781426 | 2 |
| C2×#100×C163 | 2 |
| #2002 | 163 |